College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.8 - Function Operations and Composition - 2.8 Exercises - Page 266: 2

Answer

$(f+g)(-5)=44$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $ (f+g)(-5) ,$ given \begin{array}{l}\require{cancel} f(x)=x^2+3 \\ g(x)=-2x+6 ,\end{array} use the definition of the appropriate function operation. Then substitute $x$ with $ 3 .$ $\bf{\text{Solution Details:}}$ Since $(f+g)(x)=f(x)+g(x),$ then \begin{array}{l}\require{cancel} (f+g)(x)=(x^2+3)+(-2x+6) \\\\ (f+g)(x)=x^2+3-2x+6 \\\\ (f+g)(x)=x^2-2x+9 .\end{array} Substituting $x$ with $ -5 ,$ then \begin{array}{l}\require{cancel} (f+g)(-5)=(-5)^2-2(-5)+9 \\\\ (f+g)(-5)=25+10+9 \\\\ (f+g)(-5)=44 .\end{array}
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